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Optimal block replacement policies with multiple choice at failure

Part of: Operations research and management science Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Shey-Huei Sheu
Shey-Huei Sheu*
Affiliation:
National Taiwan Institute of Technology
*
∗ Postal address: Department of Industrial Management, National Taiwan Institute of Technology, 43, Keelung Road, Section 4, Taipei, Taiwan 10772.
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Abstract

A generalization of the block replacement policy (BRP) is proposed and analysed. Under such a policy, an operating system is preventively replaced at times kT (k = 1, 2, 3, ···), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of the ith minimal repair of the new subsystem at age y depends on the random part C(y) and the deterministic part ci(y). The mathematical model is defined and general analytical results are obtained.

Keywords

MAINTENANCERELIABILITYREPAIR

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.) 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 129 - 141
Copyright
Copyright © Applied Probability Trust 1992 

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References

[1]Barlow, R. E. and Hunter, L. C. (1960) Optimum preventive maintenance policies. Operat. Res. 8, 90–100.Google Scholar
[2]Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[3]Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
[4]Beichelt, F. (1981) A generalized block-replacement policy. IEEE Trans. Reliability 30, 171–172.Google Scholar
[5]Berg, M. and Cléroux, R. (1982) The block replacement problem with minimal repair and random repair costs. J. Stat. Comput. Simul. 15, 1–7.Google Scholar
[6]Berg, M, Bienvenu, M. and Cléroux, R. (1986) Age replacement policy with age-dependent minimal repair. Infor 24, 26–32.Google Scholar
[7]Bhat, B. R. (1969) Used item replacement policy. J. Appl. Prob. 6, 309–318.Google Scholar
[8]Blanning, R. W. (1965) Replacement strategies. Operat. Res. Quart. 16, 253–254.Google Scholar
[9]Block, H. W., Borges, W. S. and Savits, T. H. (1985) Age-dependent minimal repair. J. Appl. Prob. 22, 370–385.Google Scholar
[10]Block, H. W., Borges, W. S. and Savits, T. H. (1988) A general age replacement model with minimal repair. Naval Res. Logist. 35, 365–372.Google Scholar
[11]Boland, P. J. (1982) Periodic replacement when minimal repair costs vary with time. Naval Res. Logist. Quart. 29, 541–546.Google Scholar
[12]Boland, P. J. and Proschan, F. (1982) Periodic replacement with increasing minimal repair costs at failure. Operat. Res. 30, 1183–1189.Google Scholar
[13]Brown, M. and Proschan, F. (1983) Imperfect repair. J. Appl. Prob. 20, 851–859.Google Scholar
[14]Cléroux, R., Dubuc, S. and Tilquin, C. (1979) The age replacement problem with minimal repair and random repair cost. Operat. Res. 27, 1158–1167.Google Scholar
[15]Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
[16]Crookes, P. C. I. (1963) Replacement strategies. Operat. Res. Quart. 14, 167–184.Google Scholar
[17]Ait Kadi, D. and Cléroux, R. (1988) Optimal block replacement policies with multiple choice at failure. Naval Res. Logist. 35, 99–110.Google Scholar
[18]Marshall, A. W. and Olkin, I. (1967) A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30–44.Google Scholar
[19]Murthy, D. N. P. and Nguyen, D. G. (1982) A note on extended block replacement policy with used items. J. Appl. Prob. 19, 885–889.Google Scholar
[20]Nakagawa, T. (1981) A summary of periodic replacement with minimal repair at failure. J. Operat. Res. Soc. Japan24, 213–227.Google Scholar
[21]Nakagawa, T. (1982) A modified block replacement with two variables. IEEE Trans. Reliability 31, 398–400.Google Scholar
[22]Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[23]Savits, T. H. (1988) Some multivariate distributions derived from a non-fatal shock model. J. Appl. Prob. 25, 383–390.Google Scholar
[24]Shaked, M. and Shanthikumar, J. G. (1986) multivariate imperfect repair. Operat. Res. 34, 437–448.Google Scholar
[25]Sheu, S. H. (1987) Imperfect Repair Models In Reliability Theory. D. Sc. Thesis, University of Kentucky.Google Scholar
[26]Sheu, S. H. and Griffith, W. S. (1991) Multivariate age dependent imperfect repair. Naval Res. Logist. To appear.Google Scholar
[27]Tango, T. (1978) Extended block replacement policy with used item. J. Appl. Prob. 15, 560–572.Google Scholar
[28]Tango, T. (1979) A modified block replacement policy using less reliable items. IEEE Trans. Reliability 5, 400–401.Google Scholar